Blow-up problem for semilinear heat equation with absorption and a nonlocal boundary condition |
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Authors: | Alexander Gladkov Mohammed Guedda |
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Institution: | a Department of Mathematics, Vitebsk State University, Moskovskii pr. 33, 210038 Vitebsk, Belarusb Université de Picardie, LAMFA, CNRS, UMR 6140, 33 rue Saint-Leu, F-80039, Amiens, France |
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Abstract: | In this paper we consider a semilinear parabolic equation ut=Δu−c(x,t)up for (x,t)∈Ω×(0,∞) with nonlinear and nonlocal boundary condition u∣∂Ω×(0,∞)=∫Ωk(x,y,t)uldy and nonnegative initial data where p>0 and l>0. We prove some global existence results. Criteria on this problem which determine whether the solutions blow up in finite time for large or for all nontrivial initial data are also given. |
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Keywords: | Semilinear heat equation Nonlocal boundary condition Blow-up |
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